.. _vehicle_controller:

Control
========

The :py:class:`~highway_env.vehicle.controller.ControlledVehicle` class implements a low-level controller on top of a :py:class:`~highway_env.vehicle.kinematics.Vehicle`, allowing to track a given target speed and follow a target lane.
The controls are computed when calling the :py:meth:`~highway_env.vehicle.controller.ControlledVehicle.act` method.

Longitudinal controller
-----------------------

The longitudinal controller is a simple proportional controller:

.. math::
    a = K_p(v_r - v),

where

- :math:`a` is the vehicle acceleration (throttle);
- :math:`v` is the vehicle velocity;
- :math:`v_r` is the reference velocity;
- :math:`K_p` is the controller proportional gain, implemented as :py:attr:`~highway_env.vehicle.controller.ControlledVehicle.KP_A`.

It is implemented in the :py:meth:`~highway_env.vehicle.controller.ControlledVehicle.speed_control` method.

Lateral controller
-----------------------

The lateral controller is a simple proportional-derivative controller, combined with some non-linearities that invert those of the :ref:`kinematics model <vehicle_kinematics>`.

Position control
~~~~~~~~~~~~~~~~

.. math::
    v_{\text{lat},r} &= -K_{p,\text{lat}} \Delta_{\text{lat}}, \\
    \Delta \psi_{r} &= \arcsin \left(\frac{v_{\text{lat},r}}{v}\right),

Heading control
~~~~~~~~~~~~~~~~

.. math::
    \psi_r &= \psi_L + \Delta \psi_{r}, \\
    \dot{\psi}_r &= K_{p,\psi} (\psi_r - \psi), \\
    \delta &= \arcsin \left(\frac{1}{2} \frac{l}{v} \dot{\psi}_r\right), \\

where

- :math:`\Delta_{\text{lat}}` is the lateral position of the vehicle with respect to the lane center-line;
- :math:`v_{\text{lat},r}` is the lateral velocity command;
- :math:`\Delta \psi_{r}` is a heading variation to apply the lateral velocity command;
- :math:`\psi_L` is the lane heading (at some lookahead position to anticipate turns);
- :math:`\psi_r` is the target heading to follow the lane heading and position;
- :math:`\dot{\psi}_r` is the yaw rate command;
- :math:`\delta` is the front wheels angle control;
- :math:`K_{p,\text{lat}}` and :math:`K_{p,\psi}` are the position and heading control gains.

It is implemented in the :py:meth:`~highway_env.vehicle.controller.ControlledVehicle.steering_control` method.

API
----

.. automodule:: highway_env.vehicle.controller
    :members: